OFFSET
1,5
COMMENTS
For a given partition cn(i,n) means the number of its parts equal to i modulo n.
Short: (1=4 := 0).
a(n) is the number of partitions with parts congruent to 0, 2 or 3 mod 5. - George Beck, Aug 08 2020
LINKS
Jinyuan Wang, Table of n, a(n) for n = 1..1000
FORMULA
Convolution inverse of A113428. - George Beck, May 21 2016
G.f.: Product_{k>=1} 1/((1 - x^(5*k)) * (1 - x^(5*k - 2)) * (1 - x^(5*k - 3))). - Vaclav Kotesovec, Jul 05 2016
a(n) ~ exp(Pi*sqrt(2*n/5)) / (2*sqrt(2*(5+sqrt(5)))*n). - Vaclav Kotesovec, Jul 05 2016
MAPLE
c := proc(L, i, n)
local a, p;
a := 0 ;
for p in L do
if modp(p, n) = i then
a := a+1 ;
end if;
end do:
a ;
end proc:
A036822 := proc(n)
local a , p;
a := 0 ;
for p in combinat[partition](n) do
if c(p, 1, 5) = 0 then
if c(p, 4, 5) = 0 then
a := a+1 ;
end if;
end if;
end do:
a ;
end proc: # R. J. Mathar, Oct 19 2014
MATHEMATICA
nmax = 50; Rest[CoefficientList[Series[Product[1/((1 - x^(5*k)) * (1 - x^(5*k-2)) * (1 - x^(5*k-3))), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 05 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved